The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  X  1  1  1  1  1  1 X^3  1  1  1  1  1  1  1  1  X  X  X  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2  0  0 X^2 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3  0 X^2 X^2  0 X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3  0  0 X^3  0 X^3+X^2 X^3+X^2  0 X^3 X^3+X^2 X^2 X^3  0  0 X^3+X^2 X^2  0 X^3  0 X^3 X^3+X^2 X^3+X^2  0  0
 0  0 X^3  0  0  0  0  0 X^3  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0  0  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3  0  0  0  0  0 X^3  0  0
 0  0  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0  0  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3  0 X^3  0  0  0 X^3  0  0  0  0  0

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+27x^72+20x^73+33x^74+60x^75+45x^76+124x^77+551x^78+420x^79+540x^80+84x^81+24x^82+12x^83+15x^84+20x^85+21x^86+12x^87+12x^88+8x^89+10x^90+8x^91+1x^146

The gray image is a linear code over GF(2) with n=632, k=11 and d=288.
This code was found by Heurico 1.16 in 0.656 seconds.